Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23782470 | C2 | semidirect |
| 2. #23782469 | C2 | semidirect |
| 3. #23782466 | C2 | semidirect |
| 4. #23782040 | C2 | semidirect |
| 5. #23781936 | C2 | semidirect |
| 6. #23781934 | C2 | semidirect |
| 7. #23781835 | C2 | semidirect |
| 8. #23781831 | C2 | semidirect |
| 9. #23781781 | C2 | semidirect |
| 10. #23781780 | C2 | semidirect |
| 11. #472×C163 | C2 | semidirect |
| 12. #19104781 | C22 | semidirect |
| 13. #19104780 | C22 | semidirect |
| 15. #19104763 | C22 | semidirect |
| 16. #19104763 | C22 | semidirect |
| 18. #19104761 | C22 | semidirect |
| 27. C2×D1304 | C22 | semidirect |
| 28. C2×#14579684 | C22 | semidirect |
| 31. #19104743 | C22 | semidirect |
| 32. #19104741 | C22 | semidirect |
| 33. #19104731 | C22 | semidirect |
| 34. #19104670 | C22 | semidirect |
| 35. #19104662 | C22 | semidirect |
| 36. #19104661 | C22 | semidirect |
| 37. #19104661 | C22 | semidirect |
| 38. #19104651 | C22 | semidirect |
| 39. C8×Dic163 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C163 | C22 | semidirect |
| 41. C2×D8×C163 | C22 | semidirect |
| 42. #131×C163 | C22 | semidirect |
| 43. #108×C163 | C22 | semidirect |
| 44. #100×C163 | C22 | semidirect |
| 59. Dic652 | D4 | semidirect |
| 60. #14579689 | D4 | semidirect |
| 63. #14579688 | D4 | semidirect |
| 65. #14579687 | D4 | semidirect |
| 66. #14579686 | D4 | semidirect |
| 71. D1304 | D4 | semidirect |
| 75. #14579684 | D4 | semidirect |
| 153. C163 | #3292 | semidirect |
| 161. #472 | D163 | semidirect |
| 175. AGL(1,ℤ/8) | C2×D163 | semidirect |
| 186. C2×D8 | C2×D163 | semidirect |
| 189. #131 | C2×D163 | semidirect |
| 192. #108 | C2×D163 | semidirect |
| 197. #100 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782470 | 2 |
| #23782469 | 2 |
| #23782466 | 2 |
| #23782040 | 2 |
| #23781936 | 2 |
| #23781934 | 2 |
| #23781835 | 2 |
| #23781831 | 2 |
| #23781781 | 2 |
| #23781780 | 2 |
| #472×C163 | 2 |
| #3292 | 163 |